In reply to Indus:
A one piece tri suit is the most convenient thing to wear. You get over the embarrassment quickly as many others will be wearing one as well.
Swim in it, out of pool in bare feet and run to transition whilst you take goggles and hat off (the race organisers give everyone a hat for identification at most triathlons).
At transition have towel on ground and quickly shoogle feet about on it to dry and get any grit off, put on helmet and bike shoes (spd's - shouldn't be too far to run in them) and number belt then push bike to mount/ dismount line and away you go. (if you get more serious can practice having shoes clipped in and jump on bike and put shoes on as you are cycling)
I've never put on extra clothing on top of tri suit, you could have a top ready if you're concerned about being cold, you get used to starting on bike a bit cold though - it encourages you to go faster!!
At second transition, rack bike and take off helmet, take off bike shoes and pull on trainers and away you go. Pair of elastic speedlock laces are really handy to avoid faffing tying shoelaces.
http://www.amazon.co.uk/Ultimate-Performance-Elastic-Laces-Black/dp/B0083VJ...
Good idea to have trainers and bike shoes full of talc/ baby powder as it helps feet dry quicker.
I would see if you like it first and get by without spending much on new gear. But if you do get into it, wiggle do a lot of starter tri gear you can't go wrong with:
http://www.wiggle.co.uk/2xu-active-trisuit/
http://www.wiggle.co.uk/dhb-t10-triathlon-cycling-shoe/